Papers

Deploying QKD-based secure communication at scale requires reducing duplicated optical hardware while preserving the rate of protected user data. Earlier studies established the physical feasibility of carrying CV-QKD and classical signals over shared infrastructure, motivating a quantitative comparison between optical hardware savings and the OTP-encrypted rate. We perform this comparison by defining the secure communication rate (SCR) as the rate jointly supported by secret-key generation and classical transport, and using it to optimize a shared discrete-modulation CV-QKD link. The model combines a binomial 64-QAM security bound with a trusted receiver, protocol traffic, spectral leakage - optical power leaking into the quantum receive band - and Raman scattering. At 25 km, the asymptotic model gives an optimized SCR of 12.079 Mbps, compared with 12.095 Mbps for a separated-link reference, while reducing the transmitter and fiber counts from two to one each in the modeled direction. Increasing channel separation suppresses spectral leakage, but the resulting SCR gain diminishes once receiver bandwidth limits the rate. Under the adopted receiver-noise law, increasing the bandwidth budget from 350 to 750 MHz raises the projected 25-km SCR to 24.535 Mbps despite higher trusted electronic noise. For the studied metropolitan link, sharing saves optical resources with little rate loss, while receiver-bandwidth improvements provide greater benefit than further spectral separation. Together, these results suggest an integration path: share the transmitter and fiber, limit unwanted classical power in the quantum receive band, and increase usable receiver bandwidth where the noise budget permits.

We characterize compactness of the Hilbert-Schmidt semigroups induced by finite-mode Gaussian quantum Markov semigroups with a faithful normal invariant state. A unitary second-quantization representation for every $ s $-embedding shows that compactness at one positive time, compact resolvent, drift stability, and uniqueness of the normal invariant state are equivalent. These conditions imply immediate trace-class membership for all embeddings. We derive exact trace-norm and Hilbert–Schmidt norm formulas, an embedding-independent trace identity, and the generator spectrum with algebraic multiplicities. Examples show that compactness does not require the existence of a spectral gap and that a spectral gap need not imply compactness when the invariant state is not unique.

An important goal of high-energy physics is to better understand the spacetime structure of particle emitting sources created in heavy-ion collisions. For a fraction of a second a special form of matter, the so-called quark-gluon plasma (QGP) is created, which can be examined with the toolkit of femtoscopy. With the measurement of correlation functions it was determined that Lévy distributions describe the shape of QGP sources the most accurately, however, based on hydrodynamics Gaussian distributions are typically expected. In this article we showcase an exact solution of the equations of relativistic hydrodynamics, which aims to resolve this puzzle by providing Lévy distributions directly from hydrodynamics. A detailed analysis reveals whether the predictions of this solution are in accordance with observations.

The present paper sets out a general method for extending the isoscattering, non-isospectral quantum graphs. The methodology is illustrated by considering two graphs, denoted by $\Gamma_1$ and $\Gamma_2$, which have the same total metric length but different topologies. It is demonstrated that, despite the fact that their scattering matrices are identical, their eigenvalues, denoted by $k_n$, and Euler characteristics differ from one another. The next step in the process is to extend both graphs by affixing the same star graph to each of them. Utilising the Titchmarsh-Weyl M-function formalism, it is proven that the newly constructed, extended graphs are also isoscattering and non-isospectral.

YbZn2GaO5 has recently emerged as a structurally ideal triangular-lattice antiferromagnet and a promising candidate for hosting a U(1) Dirac quantum spin-liquid (QSL) ground state. However, signatures of broadened crystal electric field (CEF) excitations have raised questions about potential site disorder and its impact on the intrinsic spin dynamics. In this study, we employ 71Ga nuclear magnetic resonance (NMR) and muon spin relaxation (muSR) to microscopically probe both the structural and magnetic properties of YbZn2GaO5. NMR spectra reveal two inequivalent 71Ga sites and a broad distribution of quadrupolar frequencies, providing clear evidence of Ga$^{3+}$/Zn$^{2+}$ site mixing and local CEF randomness. The NMR spin-lattice relaxation rate exhibits, down to 1.3~K, a power-law temperature dependence, consistent with persisting spin dynamics below the exchange energy scale in a frustrated magnet. Complementary muSR measurements further show that the spin dynamics persist down to 30mK, with no signs of spin freezing. Together, these results establish that YbZn2GaO5 presents substantial structural disorder, while the persistence of dynamic spin fluctuations down to the lowest temperatures may indicate the survival of QSL-like excitations despite such disorder.

We show that H–F edge complexes in biphenylene nanoribbons act as intrinsic atomic resonators, flattening low-frequency phonon branches. With increasing wave vector, flexural and twisting vibrations concentrate at the edges while motion of the carbon backbone is suppressed. Displacement profiles and edge-mass tuning identify a local-resonance mechanism, an atomic counterpart of a tuned mass damper. Combining machine-learned interatomic potentials, frozen-phonon calculations, and density-functional tight binding, we find that weakly dispersive modes contribute substantially to thermal band-gap narrowing. Zero-point motion shifts the calculated gap closure toward the experimentally observed ribbon widths. A hexagonal boron nitride substrate preserves the principal spectral features while reducing thermal renormalization. These results establish edge chemistry as a route to nearly flat phonon bands and connect a local atomic resonance to the electronic response of an entire nanoribbon.

Chiral gauge theories are a central focus of research in theoretical particle physics due to the parity symmetry breaking observed in the Standard Model. Left-Right Symmetric Models (LRM) explain the breaking of parity through a Spontaneous Symmetry Breaking Mechanism, predicting new $W_R$ and $Z_R$ gauge bosons. The absence of direct BSM physics detection at the LHC has driven research towards precision observables and Effective Field Theories (EFTs), particularly the SMEFT framework. Precision radiative calculations in chiral theories using dimensional regularization require a $D$-dimensional $\gamma_5$ prescription, such as the mathematically consistent Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme. However, this scheme introduces gauge symmetry-breaking terms that obstruct Slavnov-Taylor identities. A primary objective of this thesis is to provide a pedagogical introduction to cancelling these spurious anomalies via algebraic renormalization, and to derive the one-loop symmetry-restoring finite counterterms required to renormalize the four-fermion operators of the $\nu$SMEFT. Furthermore, the thesis explores UV completions like LRMs embedded in other BSM theories like the Grand Unified Theories. This embedding implies that no discrete symmetries remain at the TeV scale and allows LRMs to be treated as EFTs with the minimal scalar content needed to perform the Spontaneous Symmetry Breaking Mechanism. The second main objective is to derive robust lower bounds on the masses of the new gauge bosons and the LR scale using collider observables. This analysis is performed for both the effective and traditional LRMs, ensuring that the results are independent of other parameters of the theory.

We report [O\,iii] narrow-band imaging of an extremely large-scale nebula, the Silk Nebula, discovered by the SWONS (Super Wide-Field [O\,iii] Narrow-band Survey), together with multi-fiber medium-resolution spectroscopic data covering the H$\alpha$, [N\,ii], [S\,ii], and [O\,iii] emission lines, acquired with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) as part of the Medium-Resolution Spectroscopic Survey of Nebulae (MRS-N). Based on 2,684 high-quality spectra, we measured its physical parameters, including relative line intensities, radial velocities (RVs), and full widths at half-maximum (FWHMs). The [S\,ii]/H$\alpha$ ratio of the nebula significantly exceeds the shock-excitation threshold of 0.4. Its location in BPT diagnostic diagrams and spatial morphology of [O\,iii] both support the optical emission is dominated by shock-heated gas. The oxygen abundance is near solar and spatially uniform, consistent with a shock propagating into the ambient interstellar medium. Because [O\,iii] is the only emission line that clearly traces the nebular morphology, we base our distance estimate exclusively on the [O\,iii] kinematics, obtaining a fiducial distance of $\sim$160 pc. At this distance, the nebula has a physical extent of $\sim$28 pc along the north-south direction. We suggest that the Silk Nebula is a large [O\,iii] filament possibly associated with a supernova remnant, although a diffuse-ionized-gas (DIG) or ionized-bubble origin cannot be ruled out with the present data, and one of the largest angular-scale [O\,iii] emission structures documented to date. Future deep X-ray observations and shock-modeling efforts are required to firmly establish its nature.

We discuss General Relativity and some of its modifications as effective field theories of the breaking of the affine general linear group using the coset approach and the Maurer-Cartan form. While the ultimate goal is to break the symmetry down to the Lorentz subgroup, we argue that there are three interesting breaking cascades in which the affine general linear group is first broken to a larger subgroup that contains the Lorentz group. In all cases, the breaking of translations always generates Goldstone modes that can be interpreted as metric degrees of freedom. We argue that the effective field theories that emerge as a result of the different breaking patterns are all dynamically equivalent at the lowest order of the derivative expansion, e.g., using Einstein-Hilbert-like actions, but can differ beyond the leading order.

Extreme mass ratio inspirals (EMRIs) are promising sources for future space-based gravitational-wave detectors. We investigate EMRIs produced through the Hills mechanism, in which a stellar-mass black-hole binary (BBH) is tidally separated by a massive black hole (MBH), leaving one component bound to it. We present the first self-consistent modelling of this channel, combining an orbit-averaged Fokker-Planck treatment of the nuclear star cluster (NSC), three-body modelling of the binary-MBH encounter, Monte Carlo evolution of captured black holes (BHs), and fully relativistic EMRI trajectories to follow the evolution from binary supply down to final plunge. We find that Hills EMRIs are substantially more circular than classical EMRIs formed through two-body relaxation. For an MBH of $4 \times 10^6 M_\odot$ and circular, equal-mass BBHs of $20 M_\odot$ with initial separation of $0.1$ AU, EMRI mean eccentricities are approximately $0.097$ at our adopted LISA-band entry threshold and $0.034$ at plunge, compared with $0.478$ and $0.228$, respectively, for classical EMRIs. Of the initial BBHs, approximately $0.4$ per cent become EMRIs, whereas approximately $60$ per cent of captured BHs do. For comparable NSC initial compact-object mass, we find approximately $1.6 \times 10^{-8}$ Hills EMRIs per year per galaxy, approximately $12$ per cent of the classical EMRI yield. The Hills channel contribution to the overall eccentricity distribution depends strongly on the binary mass fraction in NSCs. We discuss implications for identifying EMRI formation channels with LISA and for quasi-periodic eruptions.

We investigate the quantum dynamics of a single ion confined in a radio-frequency (RF) Paul trap in the presence of weak octupole-induced anharmonicity, as can occur in realistic ion-trap potential. The explicitly time-dependent quadrupole potential is treated in a reference-oscillator Fock basis, allowing the effects of the RF drive and the quartic correction to be resolved directly at the level of motional-state couplings. While the quadratic RF interaction generates $\Delta n=\pm2$ transitions and Gaussian squeezing, the quartic contribution opens additional $\Delta n=\pm4$ coupling pathways. Starting from the reference-oscillator vacuum, we show that the octupole interaction broadens the even-parity Fock-state distribution and enhances the phonon-number fluctuations more strongly than the mean occupation. At the same time, the RF-induced sub-vacuum quadrature squeezing remains robust, although its magnitude and orientation are modified by the quartic interaction. The number statistics and quadrature fluctuations therefore respond differently to the same nonlinear perturbation, reflecting the distinct roles of Fock-space redistribution and phase coherence. The resulting dynamics provide a quantum-mechanical characterization of weak octupole corrections beyond the ideal quadrupole approximation and clarify how realistic anharmonicities modify nonclassical trapped-ion motion. Importantly, the motional nonclassicality remains robust against the weak octupole perturbation, as evidenced by persistent sub-vacuum quadrature squeezing and Klyshko-inequality violation. These results characterize how realistic anharmonic corrections reshape trapped-ion motion beyond the ideal quadrupole approximation.

Lagrangian Neural Networks (LNNs) learn mechanical systems from trajectory data by parameterizing a scalar Lagrangian and deriving the dynamics through the Euler-Lagrange equations, biasing the model toward motion that respects the variational structure of mechanics. The interactions studied so far have been pairwise-additive, leaving open whether LNNs can recover an irreducible many-body interaction from motion alone. We address this using the Axilrod-Teller triple-dipole interaction, the leading three-body dispersion term, whose dependence on the collective geometry of three particles cannot be represented by any sum of pairwise terms. We prescribe the kinetic energy exactly and learn only the potential, as a function of interparticle distances and angles. Combined with a signal-aware sampling strategy that concentrates training data where the three-body signal is strongest while preserving broad coverage of configuration space, this recovers the interaction from accelerations alone. The learned potential reproduces the radial scaling, angular dependence, and characteristic sign reversal of the Axilrod-Teller interaction, and generates stable trajectories. Embedding it within a pairwise Lennard-Jones potential lets us examine its observability: the three-body term is recovered once its dynamical signature exceeds the residual modeling error, which it does cleanly at amplified coupling but not at the coupling of a real noble gas, bracketing the transition between the two. Finally, symbolic regression on the trained potential, with no assumed functional form, returns the Axilrod-Teller expression with angular numerator, radial law, and coupling constant intact. An LNN with domain-specific structure can thus recover an irreducible three-body interaction from trajectories as a closed-form law, pointing toward learning interaction laws whose structure is not known a priori.

Holographic complexity is expected to capture the linear growth of black hole interiors, with quantum corrections ultimately leading to a late-time saturation. We develop a spectral formulation of holographic complexity measures associated with codimension-zero bulk regions in the framework of the complexity=anything proposal. The corresponding generating function of complexity is governed by three-point correlation functions of the density of states, establishing a direct connection between bulk geometric observables and nonperturbative Euclidean spacetime wormholes. We find that the codimension-zero holographic complexity reduces to the sum of two codimension-one contributions and exhibits a universal time evolution, characterized by an exponentially long regime of linear growth followed by saturation at the Heisenberg time. The late-time plateau is a direct result of the spectral level repulsion, a generic feature of quantum chaotic systems, thereby providing a universal mechanism for the saturation of holographic complexity. We also develop a complementary operator interpretation, in which Euclidean wormhole corrections render the semiclassical basis of fixed-complexity states overcomplete. Constructing a complete orthonormal basis then yields well-defined holographic complexity operators that reproduce the same universal time evolution. Our results establish a unified connection among black hole interiors, chaotic spectral statistics, and Euclidean wormholes in quantum gravity.

Recent numerical simulations have shown that black-hole magnetospheres evolve rapidly toward alignment between the magnetic axis and spin axis but the physical origin of this process has remained unclear. We develop an analytic theory of this alignment within resistive relativistic magnetohydrodynamics. Taking the slow-spin Blandford-Znajek monopole solution as the exterior magnetic field, we reduce the induction equation to a relaxation equation for the current-sheet inclination angle. Our analysis shows that alignment results from second-order spin effects in the Blandford-Znajek solution combined with explicit resistive dissipation. We test this prediction using resistive-GRMHD simulations at several spins and resistivities and find a regime in which the measured late-time secular decay agrees quantitatively with the analytic prediction.

We formulate perturbative Jackiw-Teitelboim gravity as an ensemble of ordinary one-dimensional Hamiltonians with a confining random potential. The leading profile reproduces the disk density of states, while connected cumulants of a single master field encode the topological expansion. After formulating the cumulant power counting required by the topological expansion, we show that the cumulants reproduce all genus-zero multi-boundary amplitudes $\mathcal Z_{0,n}$. At higher genus, we show that a renormalization scheme can be chosen consistently order by order so that imposing one-boundary polynomiality recursively reproduces the perturbative JT string equation and yields the standard JT one-boundary amplitudes $\mathcal Z_{g,1}$. The framework provides a self-contained finite-$S_0$ quantum dynamics with a discrete spectrum and unitary real time evolution, beyond a mere rewriting of the matrix integral. The same confining dynamics also underlies late-time saturation and the dynamical avoidance of the would-be black hole singularity, as shown in our earlier work.

We investigate the Casimir effect between two parallel wires in $(2+1)D$ Maxwell-Chern-Simons (MCS) electrodynamics under different boundary conditions and separated by a distance $L$. Using a functional approach in which the boundary constraints are implemented by auxiliary fields localized on the wires, we integrate out the gauge field and derive an effective boundary theory whose functional determinant allows us to compute the Casimir energy. We consider perfect electric conductor (PEC), perfect magnetic conductor (PMC), and infinitely permeable (PMC2) boundary conditions. For two PEC wires, we recover the known MCS result and show that it coincides with the result obtained in the Abelian limit of the Curci-Ferrari (CF) model, implying that the Casimir effect in this case probes the photon mass $\mu$ but not its origin. The same energy is obtained for two PMC2 wires. In sharp contrast, the Casimir energy vanishes identically for the covariant PMC condition in MCS theory, both for PMC-PMC and PEC-PMC. Since this cancellation does not occur in the CF model, it could provide a signature of the topological origin of the photon mass in $(2+1)D$. Finally, the PEC-PMC2 case yields a non-vanishing Casimir force and reproduces the known result for a perfectly conducting wire facing an infinitely permeable one. Interestingly enough, we show that for PEC-PMC2, the Casimir force in the MCS theory is smaller than the one of the CF model for any $L,\mu >0$. Our results thus show that, depending on the boundary conditions, the Casimir effect could probe not only the photon mass but also reveal signatures of its origin.

Solving combinatorial optimization problems on near-term quantum computers mainly relies on their quadratic unconstrained binary formulation. Lately, binary polynomial formulations start to take the center stage, having a better scaling with respect to the number of used qubits. However, while quadratic forms are straightforward to implement on quantum circuits, polynomial forms of degree $d$ incur in circuit depth overheads, due to the lack of $d$-qubit gates, for $d\geq 3$, on current hardware. In this paper, we study the problem of designing the shallowest quantum circuit for a given polynomial form. We formulate it as a classical binary linear problem and we prove the NP-completeness of a variant of it. On the algorithmic side, we offer a scalable and performant heuristic method to tackle it, Tempura, as well as faster binary linear problem formulations, which offer computational feasibility while sacrificing optimality. Our performance evaluation shows that the algorithms yield far shorter circuits than the state-of-the-art approaches, and Tempura is mostly comparable with them in terms of runtime.

Simulating acid-base equilibria from first principles is a tremendous challenge, as it requires modeling bond-breaking events in a complex hydrogen-bonding environment. The quantum mechanical behavior of the protons is often important, complicating simulations even further. We show that by combining state-of-the-art machine-learning potentials, accelerated sampling of the dissociation process, and an efficient estimation of nuclear quantum corrections it is possible to reliably compute the dissociation constants of different species in water. We demonstrate the transferability of this workflow, applying it successfully to the autoionization of water and to the entire ladder of the aqueous dissociation of phosphoric acid. The definition of the dissociation constant, the choice of order parameters, sampling artifacts and finite-size effects, as well as quantum nuclear effects all play a non-trivial role in determining the outcome of the calculation, so that cutting corners is likely to introduce biases that can only be compensated by fortuitous cancellations of errors.

We introduce a nonconservative nonlinear Schrödinger equation (NLSE) which includes additional nonlinear terms accounting for the pseudo-stimulated-Raman-scattering (pseudo-SRS) effect and cubic loss. An essentially novel feature of the model is the linear anti-diffusion gain, which leads to the obvious blow-up in the infinite or spatially periodic system. We consider the absorptive boundary conditions, which suppress the blow-up driven by effective convective instability in the setup. The NSLE model is derived, in the extended adiabatic approximation, from the underlying Zakharov system, which includes the viscosity term acting on its low-frequency component and the anti-diffusion gain in the high-frequency (HF) one. The latter term appears if the expansion, with respect to the deviation of the wavenumber, is performed not around the minimum-loss point (as in the usual situation), but around a maximum-loss point. Dynamics of moving solitons in the model is addressed by means of analytical and numerical methods. The sech approximation for the soliton predicts it as a stable fixed point (FP) of the system of balance equations for the HF norm and wave momentum, derived in the moving reference frame. The FP attraction basin is identified too. The predictions are corroborated by direct simulations of the full NSLE with the absorptive boundary conditions.

Ultrafast laser-assisted field emission from metallic nanotips is a promising route for generating coherent electron pulses. However, existing theoretical models often neglect many-body strong correlation effects in the emitter's electronic structure and its response to the optical field. In this work, we propose a theoretical framework based on the non-equilibrium Green's function formalism to simulate the out-of-equilibrium electron dynamics across a strongly driven matter-vacuum interface, in a one-dimensional model. Treating the tip-vacuum coupling perturbatively, we find that the interplay between strong-field emission and multi-photon emission regimes can be described in terms of a filtering of the emitter's local density of occupied states through field-dressed vacuum propagators. By including electron-electron interactions via the second-Born approximation, we show that correlation-induced modifications in the electronic structure are directly transferred to the far-field spectrum. Finally, by self-consistently solving the Dyson equation at the interface, we uncover a dynamic back-action regime driven by the optical field, characterized by a periodic polarization of the emitter, which reshapes the far-field spectrum. This shows that the non-equilibrium Green's functions approach provides a versatile framework for exploring and analyzing field emission of correlated electrons.

The Zak phase provides a fundamental geometric characterization of one-dimensional band structures and, when quantized by symmetry, serves as a bulk indicator of polarization and boundary phenomena. Conventionally, its exact quantization is tied to a global symmetry of the Bloch Hamiltonian, such as inversion or reflection symmetry. Here, we demonstrate a distinct mechanism by which the Zak phase remains exactly quantized even when the corresponding protecting symmetry is explicitly broken at the level of the full Hamiltonian. The mechanism is based on local support symmetry and destructive interference: symmetry-breaking degrees of freedom are coupled to a topological parent system in such a way that the relevant Bloch states cannot leak into them. The preserved states therefore retain their parent wave functions and inherit their quantized Zak phase exactly, despite the absence of the protecting global symmetry. We establish this mechanism for general one-dimensional insulators and demonstrate it in an inversion-broken minimal model and a reflection-broken armchair nanoribbon, where a quantized $\pi$ Zak phase and associated boundary-localized states persist. We further show that perturbations violating the exact destructive-interference condition continuously dequantize the Zak phase, while a finite regime with a near-$\pi$ Zak phase and boundary response can survive. Our results establish wave-function support, rather than global symmetry alone, as a mechanism for protecting quantized quantum geometry in one-dimensional systems.

Excitons are bound electron-hole pairs in semiconductors whose interactions influence optical properties and determine their collective behavior and emergent correlated phases. Despite the theoretical and experimental significance of these phenomena, a microscopic theory of exciton-exciton interactions that takes into account the full composite nature of these quasiparticles is lacking. Here, we present a general theory of exciton-exciton interactions that builds upon our previous publication [Physical Review B 113, 155440 (2026)], which applied only to conventional semiconductors with weak band hybridization. By contrast, the theory presented here is valid in virtually any crystalline semiconducting system and can be applied to the study of biexciton formation and correlated excitonic phases in systems where band topology, quantum geometry, and moiré effects play a significant role. In addition to the analytical theory, we also present results in simple systems with flat bands with a nontrivial quantum metric and show that the biexcitonic spectrum differs strongly from that in the case without quantum geometry. Our theory paves the way for accurate quantitative calculations of biexciton spectra and excitonic many-body phases in modern condensed-matter systems.

The $^{16}$O$(p,d)^{15}$O reaction was measured at zero degrees for incident-proton energies of 403, 604, 907 and 1209 MeV. Cross-section ratios for the 6.18-MeV (3/2$^-$) and 5.24-MeV (5/2$^+$) excited-state transitions, normalized to the ground-state transition, were previously reported in Wang et al., Phys. Lett. B 879, 140563 (2026), doi:10.1016/j.physletb.2026.140563, together with their implications for high-momentum neutron components in $^{16}$O. The present work extends that study by providing additional experimental and data-analysis details, and by reporting for the first time the ratio $R_{7.3}$, defined as the cross section populating the 7.28-MeV (7/2$^+$) state relative to that for the ground state. The positive-parity state ratios exhibit a pronounced momentum dependence, consistent with representative variational Monte Carlo trends.

We analytically study the peak statistics of an amplitude ensemble to identify the local mechanism responsible for peak repulsion. Our analytical approaches show that a smooth, nondegenerate ensemble of sufficiently differentiable amplitudes exhibits quartic nearest-neighbor repulsion, $p_{\rm nn}(S)\sim S^4$, where $S$ is the spacing between adjacent peaks. We verify this prediction numerically for the tree-level highly excited string scattering amplitudes. Interestingly, we find the quartic repulsion to be robust by varying both the underlying ensemble and the amplitude functions, whereas a tunable cusp model shows that weakening differentiability changes the strength of the repulsion. Peak repulsion therefore defines a local universality class that is not unique to string theory and may occur in amplitude ensembles in other theories.

Lagrangian Neural Networks (LNNs) learn dynamics from trajectory data by parameterizing a scalar Lagrangian and deriving accelerations through the Euler–Lagrange equation, providing a variational inductive bias that improves physical consistency over purely data-driven models. LNNs have recently been extended to general relativistic settings, leaving Schwarzschild geodesics as an open challenge. Training on complex relativistic systems is hindered by the diversity of the dynamics, as well as numerical instabilities and the difficulty of adequately sampling physically relevant, diverse orbital regimes. We introduce two coordinated improvements: a decoupled position–velocity normalization scheme that independently rescales each coordinate and its time derivatives, reweighting acceleration targets to balance contributions across all channels; and an energy-constrained log-uniformly sampled dataset generation strategy informed by the innermost stable circular orbit (ISCO) structure. With these improvements, our model accurately reproduces perihelion precession and relativistic time dilation, conserves energy and angular momentum to within a few percent even after completing multiple orbits around the central mass and predicts orbital trajectories across eight orbital scenarios in close, medium, and far-field regimes. These results establish that LNNs, augmented with physically motivated normalization and sampling, can reliably learn geodesic dynamics in curved spacetime. Our work also represents the first successful training of LNNs on Schwarzschild geodesics and offers a promising direction for data-driven modeling of complex relativistic systems.

We study how a neural network reorganizes its learned function as training proceeds and as previously unseen parity data accumulate. The trained model is itself a Boolean function on binary strings of finite length. We then evaluate it on all data, inside and outside the training set, and read off its complete sign table. Its $\pm1$ entries are the amplitudes of a normalized state, dubbed the function-state, whose inverse subsystem purity $K_f=1/\textrm{Tr}(\rho_A^2)$ is an effective Schmidt rank. We find that small data additions broaden the Schmidt spectrum, whereas larger additions reconcentrate it in the target mode. The former is called differentiation because the model distinguishes inputs more sharply. The latter is called target-selective recoherence, where the model settles on the single rule shared by the added data. As the dataset grows, the connectivity of the constraint graph defined by the training set increases monotonically, whereas the learned inverse purity changes nonmonotonically. On a fixed connected dataset, as learning proceeds, the Schmidt spectrum begins to reorganize, followed by gains in target alignment and later by improvement in predictive accuracy. This ordering distinguishes three aspects of learning: constraint identifiability, function-state organization, and predictive accuracy. At fixed data size, a function that has already been learned can re-differentiate, an event we call retreat, without changing graph connectivity. Recovery reconcentrates the Schmidt spectrum in a similar target-selective pattern, without exact recurrence of the Boolean state. Thus the percolation of data constraints fixes the identifiable support, while the reduced state produced by training continues to reorganize even after that support stops changing.

We explore the possibility of non-resonant flavoured leptogenesis in the framework of the aligned two-Higgs doublet model augmented with two right-handed neutrinos. Considering the lightest heavy neutrino mass between 10 TeV-100 TeV, we calculate the baryon asymmetry of the universe by solving fully flavoured coupled Boltzmann equations and find that the observed baryon asymmetry can be successfully generated for lightest heavy-neutrino masses in this range without relying on resonant enhancement. We compute the flavour-dependent CP asymmetries and washouts as well. Unlike conventional analyses based on only one Higgs doublet, in this framework, both Yukawa structures associated with the scalar doublets contribute to the CP asymmetry, and their combined effect plays an essential role in realizing the observed lepton asymmetry. We find that the flavoured lepton asymmetry survives if the washout in that direction is weak. The CP asymmetries in the other flavour directions suffer strong washout. The surviving flavour-dependent lepton asymmetry becomes the main contributor to the final baryon asymmetry. We perform a comprehensive numerical analysis to identify the allowed regions of the multi-dimensional parameter space compatible with neutrino oscillation data, perturbativity of the Yukawa couplings, charged-lepton flavour violation and the observed baryon asymmetry.

We apply a two-layer thermophysical model, with water sublimating from below a dust-crust with dynamically varying depth, to simulate the water outgassing rate, dust-ejections, and non-gravitational forces and torques of comet 67P/Churyumov-Gerasimenko. The dust-depth is determined at each time-step by the balance of dehydration and subsurface pressure, leading to alternating ejections and crust build-up. This model is the first stage of implementing a fully coupled activity-fallback model that self-consistently incorporates dust-fallback into the ejection depth calculation, but already a number of conclusions can be drawn from these results. The two-layer model with only dehydration and ejections is able to reproduce much of the Rosetta outgassing, dust-ejection data and non-gravitational dynamics, particularly in the comet's more primitive southern terrain. Best agreement is found for nucleus material made up of small aggregates ($d_{agg}\sim1$ mm) with not-too-high dust-to-ice ratios ($\delta\sim2-8$) and low average strengths ($\lesssim1$ Pa) that decreases with depth. Disagreements between the observations and model are greatest for the northern-facing and dust-covered terrains, suggesting the importance of surface modification by fallback and material processing here, which will be the subject of investigation in the next paper.

We present an explicit quantum circuit that constructs a block encoding of a generator-representable semiseparable (one-pair) matrix directly from its two generators. For an $N\times N$ semiseparable matrix with $N=2^{n}$, the circuit uses $2n+2$ ancilla qubits and has $O({\rm polylog} N)$ depth, and it realizes a $(2\sqrt{N},\,2n+2,\,2 \sqrt{2}\ \varepsilon)$-block encoding, where $\varepsilon$ is controlled by the accuracy of the state-preparation routines that load the generators. The building blocks of the circuit are cyclic shifts, swaps, and Hadamard gates, each admitting an efficient implementation through the binary decomposition of the relevant indices.

This study aims to determine asteroid rotation periods from sparse, unevenly sampled, multi-observatory photometry using the Lomb-Scargle (L-S) method. The photometric measurements of the asteroids are taken from the circulars of the Minor Planet Center (MPC). Twelve asteroids, four of them with known rotation periods, were analyzed with two complementary methods. In the separate dataset analysis (S-method), each observatory dataset was analyzed separately, and the final period was obtained as a weighted average of the consistent candidate periods, with weights based on the peak power of the power spectrum, the number of measurements, and the quality of the corresponding light curve fit. In the combined dataset analysis (C-method), all measurements were corrected for the biases of the photometric band, the star catalog and the observatory, reduced to a common scale and merged into a single dataset, after which the period was derived directly from the L-S analysis of the combined time series. Both methods produced consistent results, and they reproduced the known periods of the four test asteroids within 0.05%. The results show that the L-S method is well suited for finding rotation periods in sparse observations with uneven sampling over long time intervals. New rotation periods were found for asteroids 2968, 2971, 3081, 3473, 3716, and 4303. The period of 2968 remains ambiguous because of daily aliasing. For 3716, the most likely period is 10.474 hours, but its daily alias at 13.405 hours cannot be excluded completely. For 3173, the strongest peaks at 22.99 and 45.98 hours are probably daily aliases of a slower brightness variation. For asteroid 2607, the period agrees with a recently published value and is more precise. The approach is therefore promising for automated searches for unknown asteroid rotation periods.